Velocimeters

ABSTRACT

A differential laser Doppler velocimeter is based on the use of a modified fibre optic Sagnac Interferometer 1,2. The interferometer phase is dependent not on the target displacement, but on its velocity. The output intensity of the interferometer may be modulated by control means PC which controls loop birefringence introducing a phase bias and polarization offset between counter-propagating beams.

FIELD OF THE INVENTION

This invention relates to velocimeters and, in particular, todifferential laser Doppler velocimeters based on the use of a modifiedfibre optic Sagnac interferometer. A feature of the invention is thatthe interferometer phase is dependent not on the target displacement,but on its velocity.

BACKGROUND OF THE RELATED ART

Unlike interferometers used to measure a Doppler frequency shiftdirectly, the practical use of the Sagnac is not restricted to very highvelocities. It finds particular advantage in the measurement of highfrequency oscillatory velocities, where the direct response to velocityeffectively discriminates against unwanted low frequency components. Tooptimize the sensitivity of the interferometer, we have introduced a π/2phase bias between the two beams, using a passive technique based oncontrol of the birefringence of the fibre loop.

Fibre optic techniques in laser velocimetry are known (Jackson, D. A.,Jones, J. D. C. 1986 Fibre Optic Sensors. Optica Acta 33, 1469, Jackson,D. A., Jones, J. D. C. 1986 Extrinsic fibre optic sensors for remotemeasurement: parts one and two. Opt. and Laser Tech. 18, 243, 299). Manycommercial instruments are now available which use fibres to formflexible waveguides between a source/detector module and a remote probe.It is thus appropriate to consider further applications of fibre opticsin which their properties are exploited to facilitate optical signalprocessing of the Doppler signal. In particular, the use of fibres andfibre components allows the implementation of interferometerconfigurations which are impractical using conventional optics.

SUMMARY OF THE INVENTION

In the present work, we have considered interferometer arrangements inwhich the detected optical phase is a function of target velocity,rather than the more usual situation in which an optical intensity isamplitude modulated with a frequency proportional to target velocity. Hehave thus sought to transfer the signal processing step of frequencydiscrimination from the electronic to the optical domain.

Direct measurement of velocity is of particular value in measurements onoscillatory targets or flows. For example, consider the use of aconventional reference beam laser velocimeter (such as one having theconfiguration of a Michelson interferometer, in which the target iseffectively one mirror of the interferometer) used to measure out ofplane vibration. The phase of the interferometer is dependent on thedisplacement of the target surface, and hence for a given velocity theamplitude of the phase modulation declines as the oscillation frequencyis increased. Hence the measurement of high frequency oscillations isdifficult, and it is generally necessary to use active phase modulationtechniques to recover the high frequency signal in the presence ofunwanted larger amplitude low frequency ambient vibrations.

According to the present invention there is provided a velocimetercomprising an interferometer including a loop of fibre optic radiationguide, means for launching optical signals in opposite directions aroundsaid loop, probe means located within said loop and adapted to launchsaid optical signals from said radiation guide towards a moveabletarget, to receive said signals after reflection from said target and tore-direct said signals into said radiation guide.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described by way of examplewith reference to the accompanying drawings in which:

FIG. 1 shows a fibre optic Sagnac interferometer used in one embodimentof the invention,

FIG. 2 shows an experimental layout,

FIGS. 3(a) through 3(d) illustrate various probe configurations,

FIG. 4 is a graphical representation of measurements of signalamplitude,

FIG. 5 is a display of a network analyzer trace, and

FIG. 6 is an oscilloscope trace.

DESCRIPTION OF PREFERRED EMBODIMENTS

Referring now to FIG. 2 of the drawings, this shows a new approach basedon the fibre Sagnac interferometer. Classical interferometers have beenused to measure optical frequencies, and hence Doppler shifts, directly.For example, both Michelson and Fabry-Perot interferometers have beenemployed in this way as frequency discriminators for the measurement ofDoppler shifts. However, such a technique is appropriate only for themeasurement of very high velocities. Otherwise, very long optical pathsare required to give the necessary frequency resolution, orimpractically high finesse is demanded from a Fabry-Perot. In principleit is possible to make very long path imbalance fibre interferometers.However, such an instrument requires use of a laser source with a verylong coherence length, and the measured Doppler shift isindistinguishable from laser frequency noise.

A schematic of a fibre optic Sagnac interferometer is shown in FIG. 1.Light is guided from a source S and launch lens L by a monomode fibre 1and is amplitude divided at a directional coupler C1. Divided light thenfollows clockwise and anticlockwise paths around a loop 2, recombiningat the coupler C1. The intensities I₁, I₂ returned by the coupler armsare measured using photodetectors PD1, PD2. For an interferometer withan ideal, lossless coupler C1, any phase difference φ betweenrecombining beams modulates the output intensities by the two beaminterferometer transfer function.

    I.sub.1'2 =I.sub.01'02 (1±V.sub.1'2 cos φ)          (2,1)

where I_(01'02) are constant intensities and V_(1'2) are the fringevisibilities. In a static, non-birefringent loop the optical pathlengths for the counter-propagating waves are identical, hence φ=0. Thusthe loop acts as a reflector with reflectance dependent on visibility V,itself in turn dependent on the directional coupler's coupling ratio K.

In practice, phase shifts between counter-propagating beams can becaused by birefringence (including gyrotropic effects), rotation of theloop (fibre gyroscope) and non-uniform, dynamic path length changes inthe loop. φ can thus be written,

    φ=φB +φD                                       (2.2)

where φB is due to birefringence and φD to dynamic effects. Recovery ofphase φ from output intensity has previously been obtained by a varietyof schemes, including phase modulation within the loop with subsequentsignal processing polarization analysis of the output and the use of 3×3directional couplers.

We have taken the novel approach of using a polarization controller inthe loop to maintain phase quadrature, that is

    φB=(2N-1)π/2                                        (2.3)

N is an integer so (2.1) becomes

    I.sub.1'2 =I.sub.01'02 (1±V.sub.1'2 sin φ.sub.D)    (2.4)

These complementary outputs may be subtracted, using appropriateweighting, to yield: ##EQU1##

Phase modulation is achieved by interrupting the fibre loop near thedirectional coupler with a probe which reflects the beams from a movingtarget.

Consider two wavefronts recombining at the directional coupler at timet. These will have encountered the target at different times t-τ₁, t-τ₂,due to the asymmetrical positioning of the probe within the loop,resulting in a phase difference of

    φD=Φ.sub.2 -Φ.sub.1 =2k[x(t-τ.sub.1)-x(t-τ.sub.2)](2.6)

where x is the normal surface displacement, k=2π/λ where λ is sourcewavelength, Φ₁, Φ₂ are the absolute phases of counter-propagating waves.φ_(D) can be written ##EQU2## where

    Δτ=τ.sub.2 -τ.sub.1                      (2.8) ##EQU3## and v=average target velocity between t-τ.sub.2 and t-τ.sub.1

The phase shift is thus due to a time average of the target velocity;the averaging time Δτ is determined by the length of the fibre loop:

    Δτ=L/c                                           (2.9)

where

L=L₂ -L₁ (where L₁, L₂ are fibre lengths from C1 to probe)

n=effective index of fibre

c=speed of light in vacuo

The frequency response of phase due to velocity is now obtained byconsidering a surface vibrating with frequency fs=ω_(s) /2, so that

    x=x.sub.o sinω.sub.s t                               (2.10)

hence the normal velocity is

    v=v.sub.o sinω.sub.s t                               (2.11)

where

v_(o) =x_(o) ω_(s). Then ##EQU4## where

    τ.sub.0 =(τ.sub.1 +τ.sub.2)/2 and Δτ=τ.sub.2 -τ.sub.1

Now ##EQU5## i.e.

    φD=2kv.sub.o Δτsinc (1/2ω.sub.s Δτ) cos ω.sub.s (t-τ.sub.o)                             (2.14)

A roll-off in response occurs at about fs=1/2Δτ and nulls at fs=1/Δτ,thus determining a maximum loop delay Δτ for a required systembandwidth. The output intensity of a Sagnac interferometer may bemodulated by loop birefringence due to the introduction of phase biasand polarization offset between counter-propagating beams. Further itmay be shown that with the ability to produce an arbitrary birefringencein the loop, any arbitrary incident polarization state can have anyarbitrary phase difference imposed upon the counter-propagating waves:this is seen by referring to FIG. 1. Monochromatic light of Jones vectorE enters loop via directional coupler C₁ and is amplitude divided intofields E₁, and is amplitude divided into fields E₃ and E₄ propagatingaround the loop in opposite directions, and recombining as E₃ ', E₄ '.

Let the birefringence of the loop in the clockwise direction be given byJones Matrix J_(A). Then, due to the co-ordinate change on return,

    E.sub.3.sup. 'J.sub.A J.sub.B E.sub.3                      (2.15)

where ##EQU6## representing co-ordinate reversal by the loop.

Assuming the loop is lossless, then E₄ ' is given by

    E.sub.4.sup.' =J.sub.B J.sub.A.sup.T E.sub.4 =J.sub.B.sup.T J.sub.A.sup.T E=J.sub.A.sup.'T E.sub.4                                  (2.16)

as J_(B) is symmetric, and where J_(A) '=J_(A) J_(B)

The loop actually has attenuation e⁻αL which is considered identical forall polarization states, giving the modified forms

    E.sub.3.sup.' =e.sup.-αL J.sub.A.sup.40 E.sub.3

    E.sub.4.sup.' =e.sup.-αL J.sub.A.sup.'T E.sub.4      (2.17)

where

    E.sub.3 =(1-γ).sup.1/2 √(1-K)E.sub.1

    E.sub.4 =(1-γ).sup.1/2 KE.sub.1                      (2.18)

where K is the coupling ratio, γ is the excess loss, and the coupler isassumed non-birefringent. Therefore,

    (i E.sub.4  E.sub.3)=e.sup.-jπ/.sub.2 (1-γ)(1-K).sup.1/2 K.sup.1/2 E.sub.1  E.sub.1                                          (2.19)

(where represents Hermitian conjugate). For a general phase offset of φand identical return polarization state, we need

    (E.sub.4.sup.'  E.sub.3)=e.sup.j(Φ-π/2) (1-γ)(1-K).sup.1/2 K.sup.1/2 E .sub.1 E.sub.1                                (2.20)

    so that E.sub.1.sup.  (J.sub.A.sup.'T) J.sub.A.sup.' E.sub.1 =e.sup.jΦ E.sub.1 E.sub.1                                           (2.21)

    thus E.sub.1.sup.  ME.sub.1 =e.sup.jΦ E.sub.1.sup. E.sub.1(2.22)

    →ME.sub.1 =e.sup.jΦ E.sub.1                     (2.23)

    where M=(J.sub.A.sup.'T) J.sub.A.sup.' =J.sub.A.sup.'* J.sub.A(2.4)

This is solved for given Φ, E₁ by finding M satisfying (2.23) and thenJ_(A') satisfying (2.24).

In the Poincaresphere representation any birefringence can berepresented as a rotation of angle Γ about a given axis. The axis isthat corresponding to the two polarization eigenstates of thebirefringence, and the angle Γ is given by the difference in retardationbetween fast and slow eigenstates, i.e. Γ=2Φ. Thus any Φ, E₁ uniquelydefine M. Writing M in terms of its unit eigenvectors ##EQU7## and theireigenvalues exp(±jΦ)

    M=(E.sub.1a E.sub.1b) diag (e.sup.jΦ, e.sup.-jΦ)(E.sub.1a E.sub.1b) (2.25)

Substituting for E_(1a) E_(1b) ##EQU8## which can be used to solve(2.24) for J_(A) ^(') : ##EQU9## as required.

It should be noted that the condition E₁ M E₁ =0 is also easilysatisfied so that the undesirable condition of 50% reflection withoutinterference can be generated. A phase modulator must therefore be usedin order to monitor phase difference and fringe visibility whilstsetting up the interferometer.

The fringe visibilities V_(1'2) are products of three parameters of thelight waves returning to the coupler

1. Their relative intensities

    V.sub.int =2|E.sub.3.sup.' ||E.sub.4.sup.' |/(|E.sub.3.sup.' |.sup.2 +|E.sub.4.sup.' |.sup.2)

2. The scalar product of their polarization states,

    V.sub.pol =|E.sub.3.sup.'  E.sub.4.sup.' |

3. Their mutual coherence V_(coh) =|γ₃₄ |

Thus, assuming fibre losses for counter-propagating beams are identical,the only other effect is due to the coupler:

V₁ has V_(int) ≈1

V₂ has V_(int) ≈1([2K(1-K)]⁻¹ -1)⁻¹

A polarization controller consisting of two quarter- and one half-waveplate is capable of synthesizing any general birefringence. If theactual loop birefringence is given by J_(L), then the controller mustsynthesize J_(p) =J_(L) ⁻¹ J_(A). Then, aside from fluctuations inbirefringence, we obtain V_(pol) ≈1.

Mutual coherence depends on source coherence and path length imbalance.As path length imbalance is simply the delay due to birefringence,potentially subwavelength, its effect on V would generally be negligiblefor all but highly broadband sources.

This sensor thus has the advantage of an inherently high fringevisibility.

The phase resolution of the Sagnac depends on the following noisesources:

Detector Photocurrent Noise or Shot Noise

sets a fundamental system limit. Assuming visibility is close to 1, whenthe system is close to quadrature, the intensity incident on PD1 is

    I.sub.1 =I.sub.01 (1+sin φ.sub.D), φ.sub.D small   (2.29)

This produces a detector photocurrent ##EQU10## where q=electroniccharge

ν=frequency of source light

h=Plancks constant

η=quantum efficiency of detector (0.69 for a silicon photodetector usedat a wavelength of 633 nm)

which, measured over a bandwidth B, has a shot noise of

    i.sub.1shot =√(2qBi.sub.01)                         (2.31)

with a resultant phase error of ##EQU11## If the system has twoantiphase outputs which are subtracted so as to reduce intensityvariations, then ##EQU12## e.g. 2×10⁻⁸ rad HZ^(-1/2) at 633 nm withrecovered power of 1 mW per detector.

Laser Phase/Frequency Noise

will be converted into intensity noise by any optical path lengthimbalance in the interferometer, by

    Δφ=Δω/c

However, in this interferometer the path imbalance arises frombirefringence effects, due mainly to bend induced birefringence in thefibre coil, and is thus only a few wavelengths.

For path length imbalance ˜Nλ, N an integer, ##EQU13## so even for, sayN=5, to achieve Δφ=10⁻⁵ rad over 1 MHz we need ##EQU14## e.g. for 830nm, f=361 THz, so need Δf=100 MHz.

This is well beyond the frequency noise characteristics of, for example,diode lasers. The Sagnac is thus insensitive to slowly-varying changesin laser frequency, compared with the loop propagation time, with aresidual frequency noise floor arising from dynamic effects.

Coherent Rayleigh Noise (CRN)

due to delayed self-homodyne type mixing of the primary light andRayleigh backscattering. If primary and backscattered light occupied thesame polarization state, this would lead to a phase error of ##EQU15##where I_(ray) =Rayleigh backscattered intensity

Icirc=Circulating intensity

B=Bandwidth

f=Linewidth of source

Consider a loop of monomode fibre operated at 633 nm with an attenuationof 10 dB Km⁻¹, most of which is Rayleigh scattered.

Backscattered power into fibre will be of the order of ##EQU16## whereN.A.=fibre numerical aperture

n=fibre refractive index

So for a 200 m coil with a source having

    Δf=60 MHz (L.sub.c =5 m), .sub.φCRN =5×10.sup.-7 rad HZ.sup.-1/2

Three main approaches are available which will reduce the level of CRN:

1. Longer wavelength source to reduce Rayleigh scattering (scales 1/λ⁴)

2. Broadband source: SLED, superfluorescent fibre or using a laserdiode, stimulate a low coherence by fast frequency modulation

3. Ensure that the polarization state of the backscattered beam isorthogonal to co-propagating primary beam over as great a fibre lengthas possible.

Other noise is due to reflection from any fibre splice or discontinuityat the probe will result in the same type of delayed self-homodyne noiseas CRN. Any reflections within a few coherence lengths of each otherwill also yield output signals varying due to source frequency noise andoptical path length fluctuations within the fibre. Further, in a regionwithin a coherence length of half way round the loop backscatter will becoherent with the primary light and will result in noise at the outputwith a spectrum corresponding to fluctuation of optical path lengthwithin the loop. These effects are minimized by avoiding reflections inthe system, and following the same precautions as for coherent Rayleighnoise.

Laser amplitude noise will directly modulate any out of quadraturesignal when antiphase outputs are subtracted. It would in principle beremoved by analogue or digital division of the photodetector output byan intensity reference. Such devices do not usually have sufficientdynamic range and bandwidth however, so the preferred solution is to usea quiet source.

Three basic probe types have been considered for use in thisinterferometer: (FIG. 3) (a),(b). This shows the ideal case. Beams fromboth fibres F1,F2 are focussed on to overlapping beam waists. If thetarget is a smooth surface, efficient coupling between fibres isachieved for minimal back reflection. Disadvantages are complexity anddifficulties in alignment.

In a further embodiment FIG. 3(c), the probe beam 1s collimated, so aflat surface must be used. The system is nominally misaligned ford>focal length f but reasonable cross-coupling efficiencies can beachieved for minimal backscatter.

A still further embodiment, FIG. 3(d), is the simplest of all threeprobe types with only the most basic alignment required. The directionalcoupler DC does waste power, however, and backscattering from target isas large as the cross-coupling. The source coherence time must thereforebe much less than the loop propagation time.

We now compare the performance of above embodiments with that of theother velocity interferometers.

Consider the case where light from a source of angular frequency ω_(o)is reflected normally off a target moving with velocity v and thenanalyzed by an unbalanced Michelson interferometer, with arms of opticalpath length L₁, L₂.

After target, ω_(o) is doppler shifted to ω.sub.Γ =ω_(o) (1+2 v/c). Thephase difference between recombining beams is given by ##EQU17## so,presuming an adequate phase recovery scheme exists, the following phasedependences will be observed: ##EQU18##

This system has three clear disadvantages compared to the Sagnac, in themeasurement of low velocities:

1. It requires a source coherence length>ΔL, limiting the potentialvelocity sensitivity.

2. It cannot distinguish between frequency noise in the source anddoppler shift due to surface vibration, unless a second reference cavityis used.

3. It is extremely sensitive to changes in path length imbalance. Achange in ΔL of λ/4 results in a phase shift of π/2, leading to thestringent condition

    α(ΔL)/ΔL<<λ/4ΔL

e.g. for λ=633 nm, ΔL=150 m, λ/4ΔL≈10⁻⁹

Path length stability is a particular problem in fibre opticinterferometers, because of the strong temperature dependence of thefibre refractive index.

The Fabry-Perot interferometer has also been used with success torecover velocity information from frequency shifts and is an obviousextension of the Michelson with the same drawbacks of source coherence,sensitivity to frequency noise and stringent stability requirements.

The Sagnac interferometer offers potential as a simple, passive laserdoppler analysis (LDA) system which gives the sign as well as themagnitude of the appropriate velocity component of a seed particle.Consider such a system using probe type c:

A particle of velocity v along axis of probe, traversing the beam waist,will produce pulses at the complementary outputs of I₁ (t), I₂ (t) whereI₁ +I₂ gives the intensity of backscattered light and (I₁ -I₂)(I₁ +I₂)gives the velocity, with appropriate sign, of the particle along thebeam axis.

If interference is to take place, it is essential that the time that theparticle spends in the beam, up, τ_(p), longer than the loop delay Δτ.In order to see when this condition is fulfilled, consider a flow withseed particles of maximum velocity v_(max). The loop delay can then beset to give a maximum dynamic phase shift of ˜π/4, ensuring linearity, agood signal to noise ratio and avoiding velocity ambiguity. ##EQU19##The dimensions of the linear region L_(i) must thus be such that##EQU20## a condition which is automatically fulfilled for practicaloptical systems.

The experimental arrangement is shown in FIG. 2. It is similar to thatdescribed in the previous section with a loop 2 of length (L) ofapproximately 210 m. A number of precautions were taken to reducepotential noise sources. The source laser S was isolated from theinterferometer using a polarizer and quarter-wave plate PQ to preventreturns from the interferometer reflecting back off the laser outputcoupling mirror. Interference arising from Fabry-Perot cavities causedby Fresnel reflection at fibre-air interfaces was minimized usingindex-matching gel and microscope coverslips. Fibre connections weremade by fusion splicing to reduce other unwanted reflections. Theinterferometer was acoustically, vibrationally and thermally shielded byembedding it in foam. The purpose of the second directional coupler C2was to enable both measurement of the reflected Sagnac output andmonitoring of the power entering the loop. A response proportional totarget velocity, and hence proportional to frequency for harmonicallyoscillating targets of fixed vibration amplitude was demonstrated in`Closed-loop` tests where the experimental arrangement was that of FIG.2 without the probe section. A vibrating surface was simulated byperiodically stretching the fibre using a piezo-electric tube (PZT),wound with approximately 50 turns of fibre. The PZT frequency responsewas measured in an ancillary experiment, using a Michelson fibreinterferometer. The frequency response was found to be approximatelyflat and linear from dc up to about 10 kHz, above which frequencymechanical resonances were observed accompanied by strongnonlinearities.

Interferometer tests were carried out over the linear frequency responserange of the PZT. The two optical outputs, at PD1 and PD2, were found tovary in antiphase, in accordance with theory. This observation precludesthe possibility that the observed output was due to intensitymodulation, caused for example by bend losses in the fibre, rather thanthe predicted phase modulation. (Intensity modulation would cause theoutputs to vary in phase). The complementarity of the outputs waschecked by addition, with independent gains to compensate for the signalreduction of one output due to it traversing the additional coupler. Theaddition did indeed produce a line of reasonably constant intensity,with a slight modulation due to the non-ideal nature of the coupler C1.

The sensitivity of the interferometer was found to be dependent on theadjustment of the polarization controller, in accordance with thetheoretical prediction, such that it was possible to operate at anypoint on the transfer function and also vary the visibility of thefringes. The tests were carried out with the interferometer adjusted toits quadrature point, where it exhibits maximum sensitivity. Because thedetected optical phase in the Sagnac is a function of target velocity,we expect the output photocurrents to be amplitude modulated to a depthproportional to the PZT modulation frequency at constant PZT outputvoltage. This is illustrated by the results shown in FIG. 4 (normalizedwith respect to the PZT driver's output voltage). The superimposedstraight line corresponds to a device sensitivity of 21.2 rad/ms⁻¹.

We developed two alternative techniques to determine the absolute changein optical path distance.

The first of these we term the `Fringe Amplitude` method. By examinationof equation (2.1) we see that the detected intensity at either of theSagnac outputs at quadrature (i.e. .sub.φB =π/2) for a harmonicallyvibrating surface (i.e. .sub.ρD =.sub.ρS sin ω_(st)) is given by,

    I.sub.q =I.sub.qo [1±V.sub.q sin (φ sin ω.sub.s t)](3.1)

now, assuming φD small, the modulation amplitude of the detected signal;is given by,

    I.sub.qm =I.sub.qo V.sub.q φ.sub.s                     (3.2)

Due to the high visibility of the Sagnac output fringes, i.e. V_(q) ≈1,the induced phase shift (In radians) is this given by ##EQU21## that is,by the ratio of the actual modulated signal amplitude to the fringeamplitude.

The second empirical way of determining the phase shift induced by thePZT is by the "Harmonics" method, whereby we compare the system outputswhen the polarization controller is adjusted to set the operating pointeither at quadrature or at a turning point of the transfer function.

If the system is operated at a turning point then the extrinsic phase.sub.φB =0 and, on making the small δ_(D) approximation, the detectedsignal, ##EQU22## which is a signal modulated at twice the frequency(and hence termed the Second Harmonic) of the output at quadrature (i.e.the first harmonic). Therefore, the modulation amplitude, ##EQU23##Thus, by comparison with (3.2) and assuming V_(t) =V_(q), it followsthat the induced phase shift, ##EQU24## The phase shift φ_(s) can bepredicted using the expected values of dΦ/dV for the phase shifter andloop delay Δτ.

This type of PZT typically gives 52±5)mradV⁻¹ turn⁻¹ at low frequencies.The 52 turns used here give a predicted dΦ/dV =(2.70±0.26)radV⁻¹. Totalloop length here was estimated at (210±10)m, resulting in ΔΓ=(1.02±0.05μs) yielding, for harmonic excitation, ##EQU25##

A sample comparison of phase shift values induced in the closed-looptests calculated by both the fringe amplitude and harmonics techniquesshown in Table 1 illustrates that both methods agree with the predictionwithin experimental error. In practice the former was found moreconvenient to implement.

It is possible to calculate the peak velocity (v_(o)) of the surfaceover the propagation time of the loop (Δτ) from the induced phase shift.That is, from equation (2.14), the peak induced phase shift amplitude,##EQU26## from which v_(o) may be determined if Δτ is known.

Velocities calculated in this manner for the closed-loop tests are givenin Table 2.

Verification of the Sagnac's linear frequency response was confirmedusing a Network Analyser to sweep the PZT driver's frequency from 100 Hzto 100 kHz. The driver was shown to have constant output voltage up to10 kHz and the interferometer a corresponding linear response--shown inFIG. 5.

To show the device operating in a practical situation on a real movingsurface a probe section (design c in FIG. 3) was spliced into the loopas per FIG. 2. The probe fibres were 3 m long and the probe beams setafocal using a ×10 microscope objective lens. A reflective elementmounted on a small piezo-electric shaker (PZS) driven directly from afunction generator was used as a target. The fibre to target distancewas arbitrarly chosen to be 16 cm and the measurement volume spot radiuswas approximately 1.6 mm.

The probe was aligned to couple the counter-propagating beams back offthe target into the opposite fibres and open-loop static-mirror testsperformed at quadrature using the PZT in the loop to provide the phasemodulation showed that the system gave the same response proportional tofrequency as in the closed-loop tests but with an approximate 50%decrease in overall signal intensities due to the extra loss introducedby incomplete re-coupling back into the probe.

Vibrating mirror tests were performed at sample resonant PZS frequenciesand the induced phase shifts calculated using the Fringe Amplitudemethod. The detected phase shifts ranged from 0.02 to 0.30 radianscorresponding to peak target velocities of 1.1 mms⁻¹ to 15.6 mms⁻¹.

A typical set of antiphase outputs with vibration frequency 244 kHz isshown in FIG. 6. One output shows a modulation amplitude of (6.75±0.25)mV with a fringe amplitude of (37.5±2.5) mV and the other (4.25±0.25) mVof modulation with a full fringe of (25±5) mV. These correspond toself-consistent phase shifts of (0.18±O.O1) rad and (0.17±O.02) radsrespectively, and hence to velocities of (9.5±0.7) mms⁻¹ and (8.9+1.1)mms⁻¹ respectively.

The noise floor of the system was measured, in the absence of anexternal signal, and was found to be equivalent to a target velocity ofaround 50 nms⁻¹ Hz^(-1/2) r.m.s. in the frequency range above 100 kHz.

The Sagnac was found to give a null response at 935 kHz thus givingΔτ=1.07 μs corresponding to a loop length L=220 m.

We measured modulated signals from surfaces vibrating at frequencies inthe range 90 kHz to 1 MHz limited only by the PZT response falling offbeyond these frequencies.

The optical fibre Sagnac interferometer may be adapted to form a passivevelocimeter whose output is directly dependent on target velocity. Muchlower velocities can be measured using this technique than is achievableusing, for example, a Fabry-Perot interferometer, and the technique ismuch less sensitive to the effects of source frequency noise. He havedemonstrated the operation of a practical fibre optic Sagnac velocimeterwith a linear response for non-contacting velocity measurement ofvibrating surfaces. Its linearity was verified in tests with a simulatedvibration signal up to 10 kHz and we have shown it is possible toretrieve the signal from a real vibrating surface via a probe atfrequencies at least up to 1 MHz. Quadrature operation was maintained bya novel method involving the controlled introduction of fibrebirefringence. We have presented alternative designs which allow thetechnique to be applied in the measurement of fluid velocities.

                  TABLE 1                                                         ______________________________________                                        FRINGE          INDUCED PHASE SHIFT/rad                                       FREQ./  AMPLITUDE   HARMONICS                                                 kHz     METHOD      METHOD       PREDICTED                                    ______________________________________                                        3       0.59 ± 0.07                                                                            0.57 ± 0.10                                                                             0.46 ± 0.06                               4       0.69 ± 0.09                                                                            0.74 ± 0.14                                                                             0.61 ± 0.07                               5       0.83 ± 0.11                                                                            1.03 ± 0.18                                                                             0.76 ± 0.09                               ______________________________________                                    

                  TABLE 2                                                         ______________________________________                                        PEAK SURFACE VELOCITY/cms.sup.-1                                                      FRINGE                                                                FREQ./  AMPLITUDE   HARMONICS                                                 kHz     METHOD      METHOD       PREDICTED                                    ______________________________________                                        3       2.9 ± 0.3                                                                              2.8 ± 0.5 2.3 ± 0.3                                 4       3.4 ± 0.5                                                                              3.7 ± 0.7 3.0 ± 0.3                                 5       4.1 ± 0.5                                                                              5.1 ± 0.9 3.8 ± 0.4                                 ______________________________________                                    

We claim:
 1. Apparatus for measuring velocity comprising:aninterferometer including a loop of fibre optic radiation guide; meansfor launching optical signals from a source of radiation in oppositedirections around said loop; probe means located within said loop andadapted to launch said optical signals from said radiation guide towardsa moveable target, and to receive said optical signals after reflectionfrom said target, and to re-direct said received optical signals intosaid radiation guide.
 2. Apparatus as claimed in claim 1 furthercomprising phase control means to create a phase difference between saidoptical signals, wherein said phase control means comprises means tocontrol birefringence in said loop of fibre optic radiation guide. 3.Apparatus as claimed in claim 2 wherein said phase control meanscomprises means to control birefringence in said loop of fibre opticradiation guide.
 4. Apparatus as claimed in claim 1 wherein said phasecontrol means is adapted to introduce a phase bias of substantially π/2between said optical signals.
 5. Apparatus as claimed in claim 1including polarization control means to substantially maintain phasequadrature in said loop.
 6. Apparatus as claimed in any one of claims 1,2, 3, 4 or 5 wherein the source of radiation is isolated from theinterferometer by means of a polarizer and a quarter-wave plate. 7.Apparatus as claimed in claim 1 wherein means is provided to focus beamsfrom two fibre ends on to overlapping beam waists.
 8. Apparatus asclaimed in claim 1 wherein beams from two fibre ends are collimated. 9.Apparatus as claimed in claim 1 further comprising:coupler means forcoupling radiation from opposing arms of said probe means; and focussingmeans provided to launch and receive radiation from one only of saidopposing arms.
 10. Apparatus as claimed in claim 1 further comprisingdirectional coupler means for measuring radiation reflected from saidtarget and for measuring a power of radiation entering said loop.